Janet jumps off a high-diving platform with a horizontal velocity of 3.5 m/s and lands in the water 1.7 s later. How high is the platform, and how far from the base of the platform does she land?
When finding how high the platform is the horizontal velocity isn't important.
S= 1/2at^2 where S is the displacement and a is the acceleration due to gravity (9.8)
so
S=(1/2) (9.8) 1.7^2
S=4.9*1.7^2
S=14.161 meters
When finding how far from the base Janet lands use the formula:
D=Ut where D= the distance from the platform, U= the horizontal velocity, and t= time
So:
D=Ut
D=3.5*(1.7)
D=5.95
Simple isn't it?
Janet jumps off a high diving platform with a horizontal velocity of 2.64 m/s and lands in the water 2.8 s later. How high is the platform? The acceleration of gravity is 9.8^2 m/s. Answer in units of m
To find the height of the platform, we can use the formula for vertical displacement:
Δy = v₀y * t + (1/2) * a * t²
Where:
Δy = vertical displacement (height of the platform)
v₀y = initial vertical velocity (0 m/s, since Janet jumps off horizontally)
t = time (1.7 s)
a = acceleration due to gravity (-9.8 m/s²)
Plugging the values into the formula:
Δy = 0 * 1.7 + (1/2) * (-9.8) * (1.7)²
Simplifying:
Δy = -0.5 * 9.8 * 2.89
Δy = -14.098 meters
Since the height cannot be negative, we take the absolute value:
Δy = 14.098 meters
Therefore, the height of the platform is approximately 14.098 meters.
To calculate the horizontal distance, we can use the formula:
Δx = v₀x * t
Where:
Δx = horizontal distance
v₀x = initial horizontal velocity (3.5 m/s)
t = time (1.7 s)
Plugging in the values:
Δx = 3.5 * 1.7
Δx = 5.95 meters
Therefore, Janet lands approximately 5.95 meters from the base of the platform.
To find the height of the platform and the horizontal distance Janet lands from the base of the platform, we can use the equations of motion.
Step 1: Determine the vertical (upward/downward) motion
Since Janet jumps off the platform with a horizontal velocity and lands vertically in the water, we can analyze her vertical motion separately. We'll use the following equation of motion:
h = h0 + v0t + (1/2)gt^2
Where:
h is the final height (the height of the platform)
h0 is the initial height (0 in this case, as she starts from the platform)
v0 is the initial vertical velocity (unknown)
t is the time taken (1.7 s)
g is the acceleration due to gravity (-9.8 m/s², assuming downward direction)
Substituting the known values into the equation, we get:
h = 0 + v0 * 1.7 + (1/2) * (-9.8) * (1.7)^2
Simplifying, we have:
h = 1.7v0 - 13.333
Step 2: Determine the horizontal motion
Janet jumps off the platform with a horizontal velocity of 3.5 m/s, and she spends 1.7 seconds in the air before landing. Therefore, the horizontal distance she covers can be calculated using:
d = v0 * t
Where:
d is the horizontal distance (unknown)
v0 is the horizontal velocity (3.5 m/s)
t is the time taken (1.7 s)
Substituting the known values, we get:
d = 3.5 * 1.7
Simplifying, we have:
d = 5.95
So, Janet lands a horizontal distance of approximately 5.95 meters from the base of the platform.
Step 3: Solve for the height of the platform
Now that we have the horizontal distance, we can substitute it back into the first equation to solve for the height of the platform:
h = 1.7v0 - 13.333
0 = 1.7v0 - 13.333 - h
h = 1.7v0 - 13.333
Since we already found the horizontal distance to be 5.95 meters, we can substitute this value in the equation:
h = 1.7v0 - 13.333
0 = 1.7v0 - 13.333 - 5.95
0 = 1.7v0 - 19.283
19.283 = 1.7v0
v0 = 19.283 / 1.7
v0 ≈ 11.39
Finally, substitute the value of v0 back into the equation to find the height:
h = 1.7 * 11.39 - 13.333
Calculating, we get:
h ≈ 4.833
Therefore, the height of the platform is approximately 4.833 meters. Janet lands a horizontal distance of around 5.95 meters from the base of the platform.